Analysis Of The Extensibility Of Daubechies Density Functional In Large-Scale System Computing

Density functional electronic structure calculation is an important field in the efficient solution of large-scale architecture.The Daubechies wavelet function has good orthogonality and locality,and it is used as a basis function to solve the density functional calculation with high precision and strong parallel expansion.In the practical solution of practical computational problems,if we can allocate parallel computing resources scientifically and reasonably,the algorithm can solve electronic structures with hundreds of atomic system scales.The early development of the cubic scaling algorithm of Daubechies wavelet density functional,its algo-rithm complexity increases with the scale of the problem in a cubic order,when the atomic computation scale increases to hundreds or even thousands,it can not be allocated in the reasonable resources The calculation is completed within the effective time.In order to reduce the complexity of the algorithm,the Daubechies wavelet density functional further develops a linear scaling algorithm to meet the increasing demand for computing scale.Although to a certain extent,the severe requirements of time and space in the computational solution brought about by the increase in scale are alleviated,in the calculation of the electronic structure of the actual problem,the specific calculation process is very sensitive to the setting of the calculation parameters related to the convergence accuracy.How to effectively cal-culate the parameter optimization for the type of atomic structure it faces,so that the computational speed is fast converged and the calculation accuracy meets the research requirements.If we analyze the speedup ratio and efficiency in the specific parallel computing,ensuring that the computing application has good scalability is an important part of this study.The dissertation is based on the recent advances in the density functional of Daubechies wavelet,and solves the complexity problem of solving the Kohn-Sham equation by the cubic scaling algorithm.The complexity of the linear scaling al-gorithm is improved and compared with the application examples.Computational Parallel Extensibility Study.A large number of numerical experiments were per-formed on the calculations of different boundary conditions in the application of Daubechies density functional programs.Thirty parameters that had the greatest influence on the convergence of the calculation were selected and verified repeat-edly.These parameters were given in the paper.Ranges.The BigDFT software was used to simulate and calculate the new solar cell materials,and good scalability calculation performance was obtained.The main contents of the dissertation are as follows:(1)Analyze the algorithm complexity of the cubic scale and linear scale algorithm,and compare the develop-ment of several Daubechies wavelet density functional parallel computing software packages.The parameters and meanings corresponding to the cubic scale and the linear scaling algorithm of the BigDFT software package are introduced in detail,and the range of parameter values under the boundary condition of the calculated surface is given.(2)According to the influence of parallel computing scalability on computing performance,the efficiency factors of electronic structure calculation are analyzed,and the parallel scalability of equal load is introduced for experimental research.(3)The linear scale version of BigDFT software is optimized and compiled on the high performance computing platform.The MPI strong extension and weak extension simulation tests of the linear scaling algorithm were performed,and a good parallel scheduling strategy under this platform was obtained.Combining with re-search and analysis,the three-dimensional boundary model of new energy materials has been tested for parallel scalability and structural optimization of equal loads,and good computational performance has been obtained.The analysis conclusions of the linear scaling algorithm with good expansibility and parallel computing for large-scale systems are given.